Revealing mistake: When the gang attack the vampires in the bowling alley, watch as Jasmine and Fred walk over the bowling lanes in the background as the others fight the vampires. Jasmine slips on the floor but manages to maintain her balance. You'd think a deity with superhuman strength, telepathy, shape-shifting and psychic capabilities would be able to walk on a smooth floor without slipping and also know that it was smooth to begin with. Although she may lack friction, the shot should have been re-filmed as it is a blatant mistake.
Other mistake: The Chinese writing shown tattooed all over Wo-Pang's body is nonsense (a small number of random characters repeatedly jumbled together), although Wesley reads it as if it is language. (Although one might argue that the writing is meant to be some sort of code, there is no evidence in the show itself to suggest that, and Wesley refers to "translating" rather than "decoding" it; for these reasons it is more likely to be simply a mistake rather than an intentional decision.)
Audio problem: During Lilah's failed attempt to rescue Angelus, when Gunn shoots at Angelus with the tranquilizer gun, Angelus passes out then hits the ground. When he is about to pass out, we hear the sound effect of him hitting the ground before he even begins to fall over, and instantly in the next camera angle he hits the ground.
Continuity mistake: When Wesley tells Faith that Angelus is back, she says, "Step away from the glass" and hangs up the phone. When Wesley jumps from his chair (to allow Faith to smash through the glass and escape) you can see Faith behind the glass with her hands up to her face and standing, but in the close up of Faith her hands are at her sides and she is only just getting out of her chair.
Continuity mistake: When Fred is running from the oncoming white car, she runs toward a blue car getting fixed on the side of the road, but jumps out of the way as the white car hits the blue car. Fred hits the ground and rolls over to the fence, but in a following shot it shows Fred only just hitting the ground and she is on the grass, not next to the fence.
Continuity mistake: When Jasmine picks up the car and throws it at Angel, it cuts to a shot of Angel moving out of the way then shows the car falling from the bridge. First mistake, Jasmine disappears from the shot when the car is falling, and second, the car falls directly straight and at a higher point than Jasmine actually threw it.